A number theory problem by Saurav Pal
Number Theory
Level
2
If x= 1/7 , then
Find the sum :
1 + 6x + 7x^2 + 8x^3 + 9x^4 + 10x^5 + . . . . . . . . . upto infinity.
If the sum can be expressed as p/q
Then find (p + q).
The answer is 109.
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1 solution
S=1+6/7+7/7^2+......eq.1 Multiplying both the sides by 1/7 implies S/7=1/7+6/7^2+7/7^3+........eq2 eq.1-eq.2 gives (6/7)S=1+5/7+1/7+1/7^2+1/7^3+...... S=73/36=p/q hence p+q=109.